Question

Three bulbs $B_1,B_2$ and $B_3$ are connected to the mains as shown in the figure. If $B_3$ is disconnected from the circuit by opening switch $S$, than incandescence of bulb $B_1$ will

• A. decrease
• B. increase
• C. cannot say
• D. no change

Answer 1

The correct option is A decrease

Assuming that the 3 bulbs are identical, thus each of the bulb offers resistance of R $\Omega$. Also lets assume the overall voltage across the ends of the battery be V volts.
Initially, when the switch is closed, the total resistance of the circuit will be 1.5R $\Omega$. Thus the current across $B_1$ is $\frac{2V}{3R}$ i.e. 0.66$\frac{V}{R}$. The current across $B_2$ is equal to the current across $B_3$ and is equal to $\frac{V}{3R}$ i.e. 0.33$\frac{V}{R}$.
When the switch is open the total resistance of the circuit becomes 2R $\Omega$. Thus the current across $B_1$ is $\frac{V}{2R}$ i.e. 0.5$\frac{V}{R}$. The current across $B_2$ is also equal to $\frac{V}{2R}$ i.e. 0.5$\frac{V}{R}$.
Hence the current through the bulb $B_1$ decreases from 0.66$\frac{V}{R}$ to 0.5$\frac{V}{R}$. Thus, the incandescence of bulb $B_1$ also decreases.